Evolutionary stability of portfolio rules in incomplete markets

This paper studies the evolution of wealth shares of portfolio rules in incomplete markets with short-lived assets. Prices are determined endogenously. The performance of a portfolio rule in the process of repeated reinvestment of wealth is determined by the wealth share eventually conquered in comp...

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Bibliographic Details
Published in:Journal of mathematical economics 2005-02, Vol.41 (1), p.43-66
Main Authors: Hens, Thorsten, Schenk-Hoppé, Klaus Reiner
Format: Article
Language:English
Subjects:
Economic theory
Evolution
Evolutionary economics
Evolutionary finance
Finance
Incomplete markets
Market
Market selection
Mathematical methods
Portfolio investments
Portfolio selection
Portfolio theory
Studies
System theory
Wealth
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Summary:This paper studies the evolution of wealth shares of portfolio rules in incomplete markets with short-lived assets. Prices are determined endogenously. The performance of a portfolio rule in the process of repeated reinvestment of wealth is determined by the wealth share eventually conquered in competition with other portfolio rules. Using random dynamical systems theory, we derive necessary and sufficient conditions for the evolutionary stability of portfolio rules. In the case of Markov (in particular i.i.d.) payoffs these local stability conditions lead to a simple portfolio rule that is the unique evolutionary stable strategy. This rule possesses an explicit representation. Moreover, it is demonstrated that mean–variance optimization is not evolutionary stable while the CAPM-rule always imitates the best portfolio rule and survives.
ISSN:0304-4068
1873-1538
DOI:10.1016/j.jmateco.2003.01.001